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An alternator is a network of concurrent processes, which satisfies the following conditions. (1) If one process executes the critical step, no neighbor of the process executes the critical step in the same computing step.(2) Along any infinite computing steps, each process executes the critical step infinitely often. (3)An alternator is self-stabilizing to the above conditions. An alternator is said to be 1-fair if condition (2) is changed as: A process can execute the critical step twice only if all other processes execute the critical step at least once. In this paper, we proposed an alternator for rings of odd size. The design has the snap property in the sense that it satisfies condition (1) even when transient faults occur. The alternator allows each process execute the critical step once every three steps when it stabilizes. The design is optimal 1-fair in the sense that no other 1-fair design can have better performance. Based on the above design, we fine-tune the alternator to achieve maximal performance. That is, our final alternator is a maximal alternator: a process is allowed to execute the critical step when both its two neighbors do not execute the critical step.

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